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In other news, it is apparently economically infeasible for the states of New York and New Jersey to build another railroad tunnel under the Hudson river.

The GDP of the Faeroe islands is in the $2-3bn range, with 3% aid from Denmark. That's less than 1% of New Jersey, and closer to 3 orders of magnitude less than New York City.

The article says the new tunnels will cost €50,000 per inhabitant.

I don't know that NY/NJ need it that badly, and unlike the Faroes, what the area needs more are alternative travel methods (or more capacity for existing alternatives), not more cars.

A tunnel under the Hudson certainly would not cost anything like €50,000 per inhabitant of the affected economic zone.

By the way, did I not mention that the proposal was for a railroad tunnel? Oh, yes, I did.

Tunneling costs have nothing to do with the population size.

If NYC has 100x the population they would spend 1% as much per person for the same tunnel. At most the question is how much demand you would get and thus how large a tunnel you want. But even then you could simply build one, charge enough to pay for the next and keep going that way.

Size and complexity of tunnels increases as the population it serves does. Railroad tunnels have stricter grade and curve requirements than car tunnels, as well.

It is also already possible to get from NJ to NYC in a relatively reasonable amount of time, which makes the cost/benefit different than the Faroes turning things from half a day to minutes.

Demand is related to population size, but it's far from 1:1. Many people in NYC would have no reason to use this tunnel where presumably everyone on a small island would use it if it's replacing the existing ferry.

Further demand is also a revenue source, if 100,000 people per day to use a tunnel that's a much large revenue stream that's going to pay for a larger tunnel.

What population size directly provides is easier financing. NYC could for example build a tunnel without going into debt and then use the revenue from tolls for other things.

Did the islands pay for these tunnels themselves? How? What is the payoff period (I.e how long until the economic value of the tunnels exceeds their costs?).
Halfway down the the article, there's a bit about the Vaga tunnel, it's ownership, funding and payoff. Key points:

Vága-og Norðoyatunnilin – an independent, limited liability company fully owned by the Faroese government – was established to own and operate the Vaga tunnel.

The government provided DKK 160 million ($20.3 million) in financing, while local banks provided the remaining DKK 140 million ($17.8 million), with the tunnel and roads used as their guarantee.

Sound financial management and the unexpected popularity of the tunnels, with traffic growing 134 percent over the same amount of time, helped pay off the loan two years early.

Many highways and tunnels are being built here in the same way as well, called "public private partnership" or PPP. A private firm builds it and owns it and the government pays for the usage for say 20 years after which the government then owns it.

This has been the business idea for many instances where spending a big one time sum is politically hard, yet would be financially smart. Some have tried to sell it for many other things, for example energy saving equipment for a hospital.

The problem with getting replacement tunnels under the Hudson is the Republican party.
Forgive me I am not from this area, New York and New Jersey's elected governments are both predominantly from the Democratic Party. What do the Republicans have to do with the tunnel?
Republican governor of New Jersey Chris Christie canceled the ARC tunnel project in 2010 after work has just started. I think because he was dumb enough to think that he could use the money to reward political allies. Instead about half the money ended up applied to the California High Speed Rail project.

In 2016 when Trump came into office he canceled the replacement Gateway tunnel project. Why did Trump do that? Probably just as a fuck you to New York, no other reason.

"First Atlantic subsea roundabout".

Wow! Seems to imply there's already a non-Atlantic subsea roundabout, but my Google-fu is failing me...

Logically speaking if it is the first subsea roundabout then it is also the first Atlantic subsea roundabout. But due to how we normally communicate and interpret things one naturally might assume as you did. Our normal communication/interpretation does not follow rules of logic. It’s interesting that this is so.
That reminds me of an interesting 2017 BBC article on the Faeroe islands. Apparently women have been moving away more than men, leading to a gender imbalance. So there are 300 or so wives imported from Asian countries out of a population of 50k.

http://www.bbc.com/news/magazine-39703486

The way US funds public transport sometimes feel really silly to me. It costs $5 to drive across the Bay Bridge. Traffic is a nightmare. But it costs at least $7 for the same trip on the Bart. Bart is still at full capacity showing a clear market for it. A new tunnel would ease the traffic on the bridge and provide better public transport. But, even the so called progressive politicians talk about building a new bridge. Similarly costs are absolutely outrageous - it could cost up to $400 million just to add a bike lane to the Bay bridge.
Misspelling public as pubic once may just be a typo, no big deal. Misspelling public as pubic twice in the same post... Maybe that says something about public transport in SF.
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Driving costs total more than just bridge fare, and parking is a significant element.

That said, fair point.